We have a radial basis function $($RBF$)$ network with two hidden units and

Gaussian functions. One unit is located at $(0,0)$ and the other at $(4,4).$ The

Gaussian functions have parameter $2=1.$

a$)$ Obtain the weights of the units if the training data set is: $1=(0,0),$

$1=4$ and $2=(4,5),2=1,$ and do not use regularisation.

$10$

b$)$ For the trained network, obtain the network output when the input is

$3=(5,5).$

$4$

c$)$ Obtain the weights of the units for the training data set in a$)$ using

regularisation with parameter $=1.$

$10$

d$)$ For the trained network in c$),$ obtain the network output when the input

is $3=(5,5).$

$4$

e$)$ Considering RBFs and the multi$-$layer perceptron indicate:

i$)$ One way in which they are similar.

ii$)$ Two ways in which they are different.

$5$

Total

$33$